Simplify; express your answer in exponential form. Assume $r\neq 0, n\neq 0$. $\dfrac{{r^{4}n^{3}}}{{(r^{4}n^{3})^{3}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${r^{4}n^{3} = r^{4}n^{3}}$ On the left, we have ${r^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${r^{4} = r^{4}}$ Apply the ideas above to simplify the equation. $\dfrac{{r^{4}n^{3}}}{{(r^{4}n^{3})^{3}}} = \dfrac{{r^{4}n^{3}}}{{r^{12}n^{9}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{4}n^{3}}}{{r^{12}n^{9}}} = \dfrac{{r^{4}}}{{r^{12}}} \cdot \dfrac{{n^{3}}}{{n^{9}}} = r^{{4} - {12}} \cdot n^{{3} - {9}} = r^{-8}n^{-6}$